Answer:
after 38.8 years it will double
correct option is D 38.8 years
Explanation:
given data
population grows rate = 1.8%
to find out
how many years will it take to double
solution
we consider here initial population is x
so after 1 year population will be = (100% + 1.8% ) x = 1.018 x
and after n year population will be =
so it will double
2x =
take log both side
log 2 = n log (1.018)
n =
n = 38.853
so after 38.8 years it will double
correct option is D 38.8 years
To solve this problem it is necessary to apply the kinematic equations of motion and Hook's law.
By Hook's law we know that force is defined as,
Where,
k = spring constant
x = Displacement change
PART A) For the case of the spring constant we can use the above equation and clear k so that
Therefore the spring constant for each one is 11876.92/2 = 5933.46N/m
PART B) In the case of speed we can obtain it through the period, which is given by
Re-arrange to find \omega,
Then through angular kinematic equations where angular velocity is given as a function of mass and spring constant we have to
Therefore the mass of the trailer is 4093.55Kg
PART C) The frequency by definition is inversely to the period therefore
Therefore the frequency of the oscillation is 0.4672 Hz
PART D) The time it takes to make the route 10 times would be 10 times the period, that is
Therefore the total time it takes for the trailer to bounce up and down 10 times is 21.4s